I have the functional form y= β + ε I'm trying to calculate Var(ε|X) and know that Var(ε|X) = E(εε'|X) as usual. But in calculating E(εε'|X), there's a problem I keep running into.
Here's what I did: E(εε'|X)= E(yy'-yβ'-βy'+ββ'|X)
(then expand out the y's)
= E(ββ'+εβ'+ βε'+ εε' + ....|X)
= E(ββ'|X) + E(εβ'|X) + E(βε'|X)+ E(εε'|X) + E(....|X)
But then, you see that I end up with E(εε'|X) within the solution of E(εε'|X) and that shouldn't happen. That can't be possible, right?
Everything else seems correct, what might be the problem?